DFA.CANCOR (version 0.2.3)

DFA: Discriminant function analysis

Description

Produces SPSS- and SAS-like output for linear discriminant function analysis.

Usage

DFA(data, groups, variables, plot, predictive, priorprob, covmat_type, CV, verbose)

Value

If verbose = TRUE, the displayed output includes descriptive statistics for the groups, tests of univariate and multivariate normality, the results of tests of the homogeneity of the group variance-covariance matrices, eigenvalues & canonical correlations, Wilks lambda & peel-down statistics, raw and standardized discriminant function coefficients, structure coefficients, functions at group centroids, one-way ANOVA tests of group differences in scores on each discriminant function, one-way ANOVA tests of group differences in scores on each original DV, significance tests for group differences on the original DVs according to Bird et al. (2014), a plot of the group means on the standardized discriminant functions, and extensive output from predictive discriminant function analyses (if requested).

The returned output is a list with elements

rawCoef

canonical discriminant function coefficients

structCoef

structure coefficients

standCoef

standardized coefficients

standCoefSPSS

standardized coefficients from SPSS

centroids

unstandardized canonical discriminant functions evaluated at the group means

centroidSDs

group standard deviations on the unstandardized functions

centroidsZ

standardized canonical discriminant functions evaluated at the group means

centroidSDsZ

group standard deviations on the standardized functions

DFAscores

scores on the discriminant functions

anovaDFoutput

One-way ANOVAs using the scores on a discriminant function as the DV

anovaDVoutput

One-way ANOVAs on the original DVs

MFWER1.sigtest

Significance tests when controlling the MFWER by (only) carrying out multiple t tests

MFWER2.sigtest

Significance tests for the two-stage approach to controling the MFWER

dfa_class

The predicted group classifications

posteriors

The posterior probabilities for the predicted group classifications

freqs_OR

Cross-tabulation of the original and predicted group memberships

PropOrigCorrect

Proportion of original grouped cases correctly classified

chi_square_OR

Chi-square test of independence

PressQ_OR

Press's Q significance test of classifiation accuracy for original vs. predicted group memberships

rowfreqs_OR

Row Frequencies

colfreqs_OR

Column Frequencies

cellprops_OR

Cell Proportions

rowprops_OR

Row-Based Proportions

colprops_OR

Column-Based Proportions

kappas_cvo_OR

Agreement (kappas) between the predicted and original group memberships

dfa_class_CV

Classifications from leave-one-out cross-validations

freqs_CV

Cross-Tabulation of the cross-validated and predicted group memberships

PropCrossValCorrect

Proportion of cross-validated grouped cases correctly classified

chi_square_CV

Chi-square test of indepedence

PressQ_CV

Press's Q significance test of classifiation accuracy for cross-validated vs. predicted group memberships

rowfreqs_CV

Row frequencies

colfreqs_CV

Column frequencies

cellprops_CV

Cell proportions

rowprops_CV

Row-based proportions

colprops_CV

Column-based proportions

kappas_cvoCV

Agreement (kappas) between the cross-validated and original group memberships

kappas_CVP

Agreement (kappas) between the cross-validated and predicted group memberships

Arguments

data

A dataframe where the rows are cases & the columns are the variables.

groups

The name of the groups variable in the dataframe,
e.g., groups = 'Group'.

variables

The names of the continuous variables in the dataframe that will be used in the DFA, e.g., variables = c('varA', 'varB', 'varC').

plot

Should a plot of the mean standardized discriminant function scores
for the groups be produced? The options are: TRUE (default) or FALSE.

predictive

Should a predictive DFA be conducted?
The options are: TRUE (default) or FALSE.

priorprob

If predictive = TRUE, how should the prior probabilities of the group sizes be computed? The options are:
'EQUAL' for equal group sizes; or
'SIZES' (default) for the group sizes to be based on the sizes of the groups in the dataframe.

covmat_type

The kind of covariance to be used for a predictive DFA. The options are:
'within' (for the pooled within-groups covariance matrix, which is the default) or
'separate' (for separate-groups covariance matrices).

CV

If predictive = TRUE, should cross-validation (leave-one-out cross-validation) analyses also be conducted? The options are: TRUE (default) or FALSE.

verbose

Should detailed results be displayed in console?
The options are: TRUE (default) or FALSE.

Author

Brian P. O'Connor

Details

The predictive DFA option using separate-groups covariance matrices (which is often called 'quadratic DFA') is conducted following the procedures described by Rencher (2002). The covariance matrices in this case are based on the scores on the continuous variables. In contrast, the 'separate-groups' option in SPSS involves use of the group scores on the discriminant functions (not the original continuous variables), which can produce different classifications.

See the documentation below for the GROUP.DIFFS function for information on the interpretation of the Bayes factors and effect sizes that are produced for the group comparisons.

References

Bird, K. D., & Hadzi-Pavlovic, D. (2013). Controlling the maximum familywise Type I error rate in analyses of multivariate experiments. Psychological Methods, 19(2), p. 265-280.

Manly, B. F. J., & Alberto, J. A. (2017). Multivariate statistical methods: A primer (4th Edition). Chapman & Hall/CRC, Boca Raton, FL.

Rencher, A. C. (2002). Methods of Multivariate Analysis (2nd ed.). New York, NY: John Wiley & Sons.

Sherry, A. (2006). Discriminant analysis in counseling research. Counseling Psychologist, 34, 661-683.

Tabachnik, B. G., & Fidell, L. S. (2019). Using multivariate statistics (7th ed.). New York, NY: Pearson.

Examples

DFA_Field=DFA(data = data_DFA_Field, 
    groups = 'Group', 
    variables = c('Actions','Thoughts'),
    predictive = TRUE, priorprob = 'SIZES', 
    covmat_type='separate', # altho better to used 'separate' for these data
    verbose = TRUE)

# \donttest{

# plots of posterior probabilities by group
# hoping to see correct separations between cases from different groups

# first, display the posterior probabilities
print(cbind(round(DFA_Field$posteriors[1:3],3), DFA_Field$posteriors[4]))

# group NT vs CBT
plot(DFA_Field$posteriors$posterior_NT, DFA_Field$posteriors$posterior_CBT, 
     pch = 16, col = c('red', 'blue', 'green')[DFA_Field$posteriors$Group],
     xlim=c(0,1), ylim=c(0,1),
     main = 'DFA Posterior Probabilities by Original Group Memberships',
     xlab='Posterior Probability of Being in Group NT',
     ylab='Posterior Probability of Being in Group CBT' )
legend(x=.8, y=.99, c('CBT','BT','NT'), cex=1.2, col=c('red', 'blue', 'green'), pch=16, bty='n')

# group NT vs BT
plot(DFA_Field$posteriors$posterior_NT, DFA_Field$posteriors$posterior_BT, 
     pch = 16, col = c('red', 'blue', 'green')[DFA_Field$posteriors$Group],
     xlim=c(0,1), ylim=c(0,1),
     main = 'DFA Posterior Probabilities by Group Membership',
     xlab='Posterior Probability of Being in Group NT',
     ylab='Posterior Probability of Being in Group BT' )
legend(x=.8, y=.99, c('CBT','BT','NT'), cex=1.2,col=c('red', 'blue', 'green'), pch=16, bty='n')

# group CBT vs BT
plot(DFA_Field$posteriors$posterior_CBT, DFA_Field$posteriors$posterior_BT, 
     pch = 16, col = c('red', 'blue', 'green')[DFA_Field$posteriors$Group],
     xlim=c(0,1), ylim=c(0,1),
     main = 'DFA Posterior Probabilities by Group Membership',
     xlab='Posterior Probability of Being in Group CBT',
     ylab='Posterior Probability of Being in Group BT' )
legend(x=.8, y=.99, c('CBT','BT','NT'), cex=1.2, col=c('red', 'blue', 'green'), pch=16, bty='n')


DFA_Sherry <- DFA(data = data_DFA_Sherry, 
                  groups = 'Group',
                  variables = c('Neuroticism','Extroversion','Openness', 
                                'Agreeableness','Conscientiousness'),
                  predictive = TRUE, priorprob = 'SIZES', 
                  covmat_type='separate', 
                  verbose = TRUE)

# plots of posterior probabilities by group
# hoping to see correct separations between cases from different groups

# first, display the posterior probabilities
print(cbind(round(DFA_Sherry$posteriors[1:3],3), DFA_Sherry$posteriors[4]))

# group 1 vs 2
plot(DFA_Sherry$posteriors$posterior_1, DFA_Sherry$posteriors$posterior_2, 
     pch = 16, cex = 1, col = c('red', 'blue', 'green')[DFA_Sherry$posteriors$Group],
     xlim=c(0,1), ylim=c(0,1),
     main = 'DFA Posterior Probabilities by Original Group Memberships',
     xlab='Posterior Probability of Being in Group 1',
     ylab='Posterior Probability of Being in Group 2' )
legend(x=.8, y=.99, c('1','2','3'), cex=1.2, col=c('red', 'blue', 'green'), pch=16, bty='n')

# group 1 vs 3
plot(DFA_Sherry$posteriors$posterior_1, DFA_Sherry$posteriors$posterior_3, 
     pch = 16, col = c('red', 'blue', 'green')[DFA_Sherry$posteriors$Group],
     xlim=c(0,1), ylim=c(0,1),
     main = 'DFA Posterior Probabilities by Group Membership',
     xlab='Posterior Probability of Being in Group 1',
     ylab='Posterior Probability of Being in Group 3' )
legend(x=.8, y=.99, c('1','2','3'), cex=1.2,col=c('red', 'blue', 'green'), pch=16, bty='n')

# group 2 vs 3
plot(DFA_Sherry$posteriors$posterior_2, DFA_Sherry$posteriors$posterior_3, 
     pch = 16, col = c('red', 'blue', 'green')[DFA_Sherry$posteriors$Group],
     xlim=c(0,1), ylim=c(0,1),
     main = 'DFA Posterior Probabilities by Group Membership',
     xlab='Posterior Probability of Being in Group 2',
     ylab='Posterior Probability of Being in Group 3' )
legend(x=.8, y=.99, c('1','2','3'), cex=1.2, col=c('red', 'blue', 'green'), pch=16, bty='n')


    
# data from Tabachnik & Fiddel (2019, p 307)
table9.1 <- '
1  87  5 31 6.4
1  97  7 36 8.3
1 112  9 42 7.2
2 102 16 45 7.0
2  85 10 38 7.6
2  76  9 32 6.2
3 120 12 30 8.4
3  85  8 28 6.3
3  99  9 27 8.2'
table9.1 <- data.frame(read.table(text=table9.1, 
                       col.names=c('group','perf','info','verbexp','age')))

DFA(data = table9.1, 
    groups = 'group', 
    variables = c('perf','info','verbexp','age'),
    predictive = TRUE, priorprob = 'SIZES', covmat_type='within', 
    verbose = TRUE)  
# }